#define WOKWI
//#include <stdio.h>
#include <stdlib.h>
//#include "pico/stdlib.h"
//#include <math.h>
//#include "pico/float.h"
//#include "pico/double.h"

// Define the true value of PI for error calculation
#define pi_True 3.14159265359

/**
 * @brief Computes PI using the Wallis product algorithm (single precision).
 * 
 * This function calculates the approximation of PI using the Wallis product algorithm for single-precision (float) numbers.
 * 
 * @param iteration Number of iterations to perform in the product.
 * @return float The approximation of PI using single precision.
 */

float singleFloat(float iteration){
    // Initialize the value of PI
    float pi=2.0;

    // Loop through the iterations of the Wallis product algorithm
    for (int i = 2; i < iteration ; i+=2)
    {
        // Multiply the current value of PI by the next product in the series
        pi = pi* ((float)i/(i-1)*(float)i/(i+1));
    }
    // Return the computed value of PI
    return pi;
}

/**
 * @brief Computes PI using the Wallis product algorithm (double precision).
 * 
 * This function calculates the approximation of PI using the Wallis product algorithm for double-precision (double) numbers.
 * 
 * @param iteration Number of iterations to perform in the product.
 * @return double The approximation of PI using double precision.
 */

double doubleFloat(double iteration){
    // Initialize the value of PI
    double pi=2.0;

    // Loop through the iterations of the Wallis product algorithm
    for (int i = 2; i < iteration; i+=2)
    {
        // Multiply the current value of PI by the next product in the series
        pi = pi* ((double)i/(i-1)*(double)i/(i+1));
    }
    // Return the computed value of PI
    return pi;
}


/**
 * @brief Main function that calculates PI using both single and double precision.
 * 
 * This function calls the `singleFloat` and `doubleFloat` functions to calculate PI using the Wallis product algorithm for both single and double precision.
 * It then calculates the error in both approximations compared to the true value of PI.
 * Finally, it prints the computed PI values and their corresponding errors.
 * 
 * @return int Return code: 0 for success.
 */

int main() {

//#ifndef WOKWI
    // Initialise the IO as we will be using the UART
    // Only required for hardware and not needed for Wokwi
    //stdio_init_all();
//#endif

    // Number of iterations 
    int iteration = 100000;

    // Calculate PI using single precision
    float pi_float = singleFloat(iteration);

    // Calculate PI using double precision
    double pi_double = doubleFloat(iteration);

    // Calculate the error for single precision approximation
    float singleError = pi_float - pi_True;

    // Calculate the error for double precision approximation
    double doubleError = pi_double - pi_True;

    // Print the results for single precision
    printf("Single precision: %f\n", pi_float);
    printf("Error(float):%f\n",singleError);

    // Print the results for double precision
    printf("Double precision: %lf\n", pi_double);
    printf("Error(double):%lf\n",doubleError); 

    // Returning zero indicates everything went okay.
    return 0;
}